function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

% Setup some useful variables
m = size(X, 1);
         
% You need to return the following variables correctly 
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a 
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the 
%               first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%
J = 0;
reg_term1 = 0;
reg_term2 = 0;

%Compute the regularization stuff
for i=(size(Theta1,1)+1):length(Theta1(:))
   reg_term1 += Theta1(:)(i)^2;
end
for i=(size(Theta2,1)+1):length(Theta2(:))
   reg_term2 += Theta2(:)(i)^2;
end


J += (lambda/(2))*(reg_term1 + reg_term2);

%Compute the NN gradient

for i=1:m
  
    %Feedforward pass
  	x = X(i, :);
	x = [1; x(:)];
	
    z2 = Theta1*(x(:));
    a2 = sigmoid(z2);
	a2 = [1;a2(:)];	
	
    z3 = Theta2*(a2(:)); 
    a3 = sigmoid(z3);

    sz3 = a3;
	
	yv = zeros(size(a3));
	yv(y(i)) = 1;
	
	%Update p
	for k=1:num_labels
	   J += -yv(k)*log(sz3(k)) - (1-yv(k))*log(1-sz3(k)); %a3=sigmoid(z3)
    end
	
	%Delta errors
	delta3 =  a3 - yv;
	delta2 = (Theta2'*delta3).*(a2.*(1-a2));
	
	Theta1_grad += delta2(2:end)*x';
	Theta2_grad += delta3*a2';
end
J /= m;
Theta1_grad /= m;
Theta2_grad /= m;

   %Compute the regularized gradient
   Theta1_grad(:, 2:end) += ((Theta1(:, 2:end))*(lambda/m));
   Theta2_grad(:, 2:end) += ((Theta2(:, 2:end))*(lambda/m));


% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end
